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B 中間子による量子もつれの検証

B 中間子による量子もつれの検証. ( submitted to PRL quant-ph/0702267 ). 物理的背景と解析・結果. One of “Exotic” topics of Belle Results. Y.Sakai KEK. 金茶会 6-July-2007. Belle detector. Mt. Tsukuba. KEKB. Belle. Ares RF cavity. ~1 km in diameter. e + source. KEKB. Integrated Luminosity.

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B 中間子による量子もつれの検証

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  1. B中間子による量子もつれの検証 ( submitted to PRL quant-ph/0702267 ) 物理的背景と解析・結果 One of “Exotic” topics of Belle Results Y.Sakai KEK 金茶会 6-July-2007

  2. Belle detector Mt. Tsukuba KEKB Belle Ares RF cavity ~1 km in diameter e+ source KEKB Integrated Luminosity ~700 fb-1 KEKB for Belle PEP-II for BaBar ~440 fb-1 8 GeV e- x 3.5 GeV e+ Lpeak = 1.71x1034 Integ. Lum. ~700 fb-1

  3. 13 countries, 55 institutes, ~400 collaborators Belle Detector • , p0 reconstruction e+-, KLidentification K/pseparation Aerogel Cherenkov Counter n = 1.015~1.030 Electromagnetic Calorimeter CsI(Tl) 16X0 3.5 GeV e+ TOF counter K/pseparation charged particle tracking 8.0 GeV e- Central Drift Chamber momentum, dE/dx 50-layers + He/C2H6 B vertex Muon / KLidentification Si Vertex Detector 4-layer DSSD KLm detector 14/15 layer RPC+Fe

  4. A B EPR Entanglement EPR Paradox: Quantum Mechanics: Entangled state  non-separable wave function even for far apart particles can not be a “complete” theory Local realistic theory with “hidden” parameters “an element corresponding to each element of reality”

  5. Bohm: Entangled states [Gedanken experiment] [D.Bohm., Quantum Theory, p614(1951)] two spin ½ particles from singlet state QM Measurement:Sx=+1/2 for apredictSx = -1/2 for b Decision of orientation of polarizer at very last moment  still above happen  No causal connection Instantaneous communication ? ( Quantum communication) Hidden parameters (Local Realistic Theory) ?

  6. A B Bell Inequality Key for experimental check ! J.S.Bell, Physics 1, 195(1964); Clauser,Horene, Shimony, Holt, PRL 23, 880(1969) Any Local realistic theory with “hidden” parameters S = |E(a,b)-E(a’,b)| + |E(a,b’)+E(a’,b’)| < 2 (Bell-CHSH Inequality) E(a,b): correlation function between measurements a and b Violation  Reject LRT, Confirm QM Many experiments performed: loopholes - Locality: need space-like measurements of A and B - Detection efficiency: sub-sample all Bell Inequality Violation = QM: ~established

  7. Bell Inequality: exp. (1) • Entangled photons [e.g. G.Weihs et al., PRL 81, 5039(1998)] (Locality loophole) A,B: 400m away, measurements <<1.3ms

  8. C++ + C---C+--C-+ Ntot E(a,b)= Cxx: # of coincidence SQM:max A: a,a’= 0, 45 deg B: b,b’= 22.5, 67.5 deg S = 2.73  0.02 14700 coincidence Bell Ineq. is violated ! Efficiency ~5%

  9. Nsam-Ndif Nsam+Ndif Bell Inequality: exp. (2) • Entangled 9Be+ ions [e.g. M.A.Rowe et al., Nature 409, 791(2001)]  ~98% (Detection efficiency loophole) (f1,f2) E(f1,f2) =

  10. Detect photons by PMT f1 = 3p/8,f2= 3p/8 E = -0.55 f1 = 3p/8,f2= -p/8 E = 0.56 S = 2.25  0.03 Bell Ineq. is violated !

  11. + B0B0 mixing _ Initial: B0 ー B0 B0 B0 _ B0 Why Y(4S)  B0B0 System _ • One of few entangled systems in HEP • Highest energy scale (~10 GeV) • breakdown of QM at high energy ? [C= -1] QM:

  12. Y(4S)  B0B0 System _ QM: Joint Probability at t1=t2 , B0B0 or B0B0 only _ _ Same Flavor (B0B0, B0B0): ∝ e-G|Dt| [1 + cos(DmDt)] Opposite Flavor (B0B0) : ∝ e-G|Dt| [1 - cos(DmDt)] _ _ _ (Dt=t1-t2) OF-SF OF+SF AQM(Dt) = = cos(DmDt)

  13. Y(4S)  B0B0 System _ Bell Inequality Test ? AQM(Dt) = cos(DmDt) E(a,b) = cos(DmDt) ? curve a: same as “Entangled photons” [includes decay rate] or E(a,b) = - e-2Gt’ e-GDt cos(DmDt) ? curve b ( t’ = Min(ta-tb) ) a b

  14. Y(4S)  B0B0 System _ [A.Bertlmann et al., PL A332, 355(2004)] Curve b should be taken Bell Inequality Test : intrinsically impossible • QM to violate Bell Inequality ; • x = Dm/G > 2.6  xd = 0.78 • Active measurement needed • Flavor measurement via decay reconstruction = passive [ some arguments may exist against above ] Any way to test QM at Y(4S) ?

  15. Belle’s Approach Precise measurement of Time-dependent Flavor Correlation • Quantitative proof of QM Entanglement • Quantitative Comparison with Non-QM model • Fully corrected (= true) A(Dt)  Direct comparison with (any) theories QM: OF-SF OF+SF AQM(Dt) = = cos(DmDt)

  16. Non-QM models (example 1) • Local Realism: Pompili & Selleri (PS) [EPJ C14,469(2004)] “elements of reality” (hidden variables) = Flavor & mass (BH, BL, BH, BL) _ _ Mass states: stable random jump of Flavor within pair Single B0: oscillation ~ 1 cos(Dmt) only determine upper/lower limits of A(t1,t2)

  17. A(Dt): PS model Integrated over tmin Note) Local realistic model with same A(Dt) as QM is possible [quant-ph/0703206]

  18. Non-QM models (example 2) • Spontaneous immediate Disentanglement (SD) [e.g. PR 49,393(1936)] separates into B0 & B0 evolve independently _ Integrated over t1+t2

  19. Analysis Method B0D*-l+n + Lepton-tag ~Same as Dm measurement [PRL,89,251,803(02),PRD 71,972003(05)] Reconstruction Vertexing: Dt = Dz/cbg ( high quality lepton-tag only) OF & SF Dt distribution • Background subtraction • Unfolding (detector resolution) Fully corrected (= true) A(Dt) • Quantitative Test for non-QM model

  20. 152M BB Signal Reconstruction signal background 6718 OF 1847 SF Background subtraction of fake D*

  21. 152M BB Background Subtraction Bin-by-bin (Dt ) for OF & SF OF SF - - 126 54 78 237 254 2 22 86 6324 1490 • Continuum: use off-Res. (negligible) • Fake D*: M(D*)-M(D0) sideband • Combinatoric D*l: “reversed l” method • B+ D**0 ln : MC • Wrong-tag correction : 1.5 0.5% (MC,data) Dt (ps)

  22. Unfolding (Deconvolution) Singular Value Decomposition (SVD) method [A.Hoecker, V.KKartvelishvile NIM A372, 469(1996)] True Dt distribution Measured Dt distribution Detector effect OF, SF separately Dt Resolution 11 Dt bins: 11 x 11 Response Matrix (using MC) (measured) = R x (true) Matrix inversion Data/MC difference included • Robustness against input: • checked by Toy MC  Sys. error

  23. Cross Check: Lifetime Fully corrected OF+SF: fit with e-Dt/t c2 = 3/11 bins t = 1.532 0.017(stat) ps consistent with PDG (1.530 0.009 ps)

  24. Results & Sys. errors Fully corrected A(Dt) Systematic Errors stat. ~ sys.

  25. 152M BB Results & fit with QM [quant-ph/0702267, submitted to PRL] Fully corrected A(Dt): fit with QM Dm = (0.501  0.009) ps-1 c2 = 5.2 (11 dof) Good ! [ fit including WA Dm = (0.496  0.014) ps-1 (excl. Belle/BaBar)]

  26. 152M BB Result: PS model difference btw. Data/Fit (points not used if PSmin < Data < PSmax ) PS Best Fit (error from Dm) Dm = (0.447  0.010) ps-1 c2 = 31.3 disfavored 5.1s over QM

  27. 152M BB Result: SD model difference btw. Data/Fit SD Best Fit (error from Dm) Dm = (0.419  0.008) ps-1 c2 = 174 disfavored 13s over QM Decoherence fraction: Fit (1-z)AQM + zASD : z = 0.029  0.057 cf) K0K0 system _ [CPLEAR, PLB 422, 339(1998) KLOE, PLB 642, 315 (2006)]

  28. Summary Quantitative study of EPR-type Flavor entanglement in Y(4S)  B0B0 decays has been performed _ • Fully corrected A(Dt) measurement •  allow Direct comparison with any theory • QM Entanglement : confirmed • Pompili-Selleri type (Local Realism) model : • disfavored by 5.1s • Spontaneous Disentanglement: rejected by 13s Bell Inequality Test might be reconsidered ?

  29. K0 system EPR: CPLEAR [PLB 422,339 (1998)] Dt=0 p p  K0K0 at rest (JPC~1- -) _ _ Dt=5cm Decoherence fraction in K0K0 basis _ z = 0.40  0.7 [PRD 60,114032 (1999)] L + K (K-id by dE/dx) OF-SF OS+SF A = Dt=0 Dt=5cm OF SF OF SF

  30. K0 system EPR: KLOE [PLB 642,315(2006)] KLOE atDAPHNE (f Factory) f KSKL(p+p-)(p+p-) 380pb-1 CPV decay Fit to Dt distribution including regeneration Decoherence fraction in K0K0 basis _ z = (0.10 0.21 0.04)x10-5 Decoherence: CP allowed decay f KSKS

  31. Time-dependent Asymmetry

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